A bandwidth limited pulse is the shortest pulse for a given spectrum, and is characterized in that all of its spectral components overlap in time (have the same phase). The duration .DELTA..pi. of a bandwidth limited pulse is inversely proportional to the width of its frequency spectrum .DELTA.v:.DELTA..tau. .varies.1/.DELTA.v. Non-bandwidth limited pulses have a frequency chirp, which has to be compensated to obtain bandwidth limited pulses. The existing compensation techniques deal mostly with pulses from mode-locked lasers. In mode-locked laser systems, chirp control and compensation is accomplished by using dispersive delay lines inside or outside the laser cavity. For this purpose prisms, diffraction gratings, Gires-Tournois interferometers, or multilayer mirrors are used inside or outside the laser cavity. One example of chirp compensation is reported in Fork et al., Opt. Lett. 12, 483 (1987), which is hereby incorporated by reference herein. A diffraction grating pair and a four prism arrangement outside the laser with respective first and second order dispersions of .about.1000 fs.sup.2 and .about.1000 fs.sup.3 were used to compensate the linear and quadratic frequency chirp. Another example in A. Stingl et al., Opt. Lett. 19, 204 (1994), which is hereby incorporated by reference herein, reports the use of specifically designed multilayer mirrors to compensate for the frequency chirp inside the cavity of a mode-locked Ti:sapphire laser. This allows first order chirp to be eliminated. The magnitude of the dispersion is .about.50 fs.sup.2 and is sufficient to achieve bandwidth-limited pulses of &lt;14 fs with the spectral width of &gt;60 nm. The ultimate achievement of these techniques was the generation of the shortest optical pulses, which are only 6-10 fs long and contain just a few optical cycles.
As discussed in Galvanauskas et al., El. Lett. 27, 2394 (1991), which is hereby incorporated by reference herein, Galvanauskas et al., Appl. Phys. Lett. 63, 1742 (1993), which is hereby incorporated by reference herein, and Galvanauskas et al., Opt. Lett. 19, 1043 (1994), which is hereby incorporated by reference herein, recent development of compact tunable lasers (e.g., three-section distributed Bragg-reflection, three-section distributed feedback, tunable twin guide, vertical-coupler, coupled-cavity laser diodes, etc.) have triggered the development of a new short pulse generation technique. This technique uses a fast tuning of the emission wavelength of a tunable laser to obtain broad bandwidth pulses, which can be compressed down to ultrashort durations. Systems using this technique have a number of properties such as robustness, compactness, reliability, arbitrary pulse repetition rate, high pulse energies and relatively low cost, which makes them an interesting and promising alternative to conventional mode-locked lasers. In the past, the demonstrated bandwidth of continuous tuning was .about.10 nm. However, the potential tuning range is as broad as the gain bandwidth of the laser medium and can exceed 100 nm, which corresponds to a bandwidth-limited duration of less than 100 fs.
The potential broad tuning range has not before been fully utilized, because the chirp nonlinearity of the pulses from a tunable laser is high, and the conventional techniques fail to compensate such chirp. In Galvanauskas et al., Opt. Lett. 19, 1043 (1994), it was demonstrated experimentally that only 1-2 nm bandwidth pulses can be compressed down to the bandwidth limit (.about.2 ps pulse duration) when a three-section DBR laser diode and a diffraction grating pair compressor are used. With additional nonlinear compression these pulses could be further shortened down to 230 fs, but the quality of the pulses is lost, in that broad pedestals and satellite pulses appear.
Fast Tuning Techniques and Chirp Nonlinearities
With fast tuning techniques, chirped pulses are generated directly from a tunable laser and compressed outside the laser cavity, as shown in FIG. 1. In general, a continuously-tunable laser contains a gain element, a phase modulator to shift the emission frequency and a tunable narrow-band filter to allow only one longitudinal mode in the cavity. To attain fast tuning, the laser cavity should be sufficiently short and the speed of the phase modulator and the tunable filter should be sufficiently high. The chirp duration can be .about.1 ns so that compression with a dispersive delay line (e.g., diffraction gratings or a standard optical fiber) would be easy. Such speed can be attained by electrical means, see A. Galvanauskas et al., Appl. Phys. Lett. Vol. 63, p. 1742-1744, 1993.
One example is a three-section tunable laser diode shown in FIG. 2a. Other possible tunable structures are also shown in FIG. 2b-f, which differ from each other via the combination of the three basic components. At present, all existing structures which can be fast wavelength tuned are semiconductor laser diodes. Wavelength tuning is performed by changing the refractive index of a semiconductor material either by varying the carrier concentration (carrier injection) or by using the electrooptic effect. In principle, other types of tunable compact laser structures, e.g., short cavity fiber lasers, waveguide lasers, and compact solid-state lasers can also be developed using integrated electrooptical, carrier-injection or other types of electrically controlled modulators and filters.
It is useful to define the chirp nonlinearity. The instantaneous frequency of a chirped pulse can be expanded into the power series: EQU .omega.(t)=.omega..sub.0 +.omega..sub.1 t+.omega..sub.w t.sup.2 +.omega..sub.3 t.sup.3 + (1)
Here .omega..sub.0 is the central frequency of the pulse, which for a bandwidth-limited pulse, should be .omega.(t).ident..omega..sub.0. Other terms, which should be absent in a bandwidth limited pulse, correspond to the first, second and higher orders of the frequency chirp respectively.
If the chirped pulses, which are generated by the fast tuning, would have only the linear term in the decomposition equation (1), bandwidth-limited pulses would be easy to attain with any linear dispersive delay line. However, a number of processes inside the cavity of a tunable laser add higher order chirp terms and typically the magnitudes of these terms are too high to be compensated by standard means.